Verifying the Decoder in RSA System: Solving for M

[ribbon]

Homework Statement

"You are to receive a message using the RSA system. You choose p = 5,
q = 7 and E = 5. Verify that D = 5 is a decoder. The encoded message
you receive is 17. What is the actual (decoded) message?"

Homework Equations

The Attempt at a Solution

N= pq = 35, our E = 5 --> M^E is congruent to R (mod35) where R is the remainder.

The decoder (D=5) is being given to me, so this shouldn't be that hard, but how can I use it to help me find M, the sent message?

 

[haruspex]

N= pq = 35, our E = 5 --> M^E is congruent to R (mod35) where R is the remainder.

The decoder (D=5) is being given to me, so this shouldn't be that hard, but how can I use it to help me find M, the sent message?

The coded message R was computed as M^E mod N. To decode, you use the same procedure but with D instead of E. Is your problem finding an efficient way to do the computation?

 

[Boorglar]

Also, even though D was given to you, you should still check that D is indeed what it is supposed to be.
I mean, to check if ED = 1 (mod the totient function).